(2x+2y+3)dx+(3y+5z)dy=0

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Solution for (2x+2y+3)dx+(3y+5z)dy=0 equation: 


Simplifying
(2x + 2y + 3) * dx + (3y + 5z) * dy = 0

Reorder the terms:
(3 + 2x + 2y) * dx + (3y + 5z) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 2x + 2y) + (3y + 5z) * dy = 0
(3 * dx + 2x * dx + 2y * dx) + (3y + 5z) * dy = 0

Reorder the terms:
(3dx + 2dxy + 2dx2) + (3y + 5z) * dy = 0
(3dx + 2dxy + 2dx2) + (3y + 5z) * dy = 0

Reorder the terms for easier multiplication:
3dx + 2dxy + 2dx2 + dy(3y + 5z) = 0
3dx + 2dxy + 2dx2 + (3y * dy + 5z * dy) = 0

Reorder the terms:
3dx + 2dxy + 2dx2 + (5dyz + 3dy2) = 0
3dx + 2dxy + 2dx2 + (5dyz + 3dy2) = 0

Solving
3dx + 2dxy + 2dx2 + 5dyz + 3dy2 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'd'.
d(3x + 2xy + 2x2 + 5yz + 3y2) = 0


Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
d = 0

Subproblem 2
Set the factor '(3x + 2xy + 2x2 + 5yz + 3y2)' equal to zero and attempt to solve:

Simplifying
3x + 2xy + 2x2 + 5yz + 3y2 = 0

Solving
3x + 2xy + 2x2 + 5yz + 3y2 = 0

Move all terms containing d to the left, all other terms to the right.

Add '-3x' to each side of the equation.
3x + 2xy + 2x2 + 5yz + -3x + 3y2 = 0 + -3x

Reorder the terms:
3x + -3x + 2xy + 2x2 + 5yz + 3y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 2xy + 2x2 + 5yz + 3y2 = 0 + -3x
2xy + 2x2 + 5yz + 3y2 = 0 + -3x
Remove the zero:
2xy + 2x2 + 5yz + 3y2 = -3x

Add '-2xy' to each side of the equation.
2xy + 2x2 + 5yz + -2xy + 3y2 = -3x + -2xy

Reorder the terms:
2xy + -2xy + 2x2 + 5yz + 3y2 = -3x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 2x2 + 5yz + 3y2 = -3x + -2xy
2x2 + 5yz + 3y2 = -3x + -2xy

Add '-2x2' to each side of the equation.
2x2 + 5yz + -2x2 + 3y2 = -3x + -2xy + -2x2

Reorder the terms:
2x2 + -2x2 + 5yz + 3y2 = -3x + -2xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 5yz + 3y2 = -3x + -2xy + -2x2
5yz + 3y2 = -3x + -2xy + -2x2

Add '-5yz' to each side of the equation.
5yz + -5yz + 3y2 = -3x + -2xy + -2x2 + -5yz

Combine like terms: 5yz + -5yz = 0
0 + 3y2 = -3x + -2xy + -2x2 + -5yz
3y2 = -3x + -2xy + -2x2 + -5yz

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -3x + -2xy + -2x2 + -5yz + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -3x + -2xy + -2x2 + -5yz + -3y2

Simplifying
0 = -3x + -2xy + -2x2 + -5yz + -3y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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